Factual error: When Wolverine is being chased after the explosion of the barn, there's a Humvee chasing the motorcycle. The movie is supposed to take place in the late 70's - the Humvee started production in 1984 and started service in the late 80's.
Continuity mistake: When Kayla 'dies', Logan leaves her body in the woods, not bothering to have a funeral or even bury her. He takes off running to the bar and it's nighttime when he arrives.
Revealing mistake: When Wolverine and Gambit are fighting, at one point Wolverine starts slicing apart a fire escape stairway Gambit is on, causing it to slowly collapse downwards. But if you pay attention, the scene is completely ridiculous. The fire-escape slowly collapses, in defiance of physics, at just the right speed for Wolverine to be able to slice it apart piece by piece (when in reality it should have fallen down all at once and then just fallen over), the pieces that Wolverine slices seem to just explode into nothingness when there should be pieces of metal building up around him, and even beyond that... The effect itself also looks very unrealistic. Poorly put together effects sequence that doesn't make any sense if you pay attention.
Revealing mistake: When the mutants all run to Xavier and the helicopter towards the end of the film, it's blatantly obvious the actors were filmed running on a green-screen and then comped into the scene. The lighting on the actors doesn't really match the background, and somewhat more noticeably, they also don't cast any shadows on the ground.
Other mistake: When Wolverine and John Wraith arrive in New Orleans, the street is jammed with people and the casino they find Gambit in is also completely full of patrons. Yet somehow Wolverine being thrown through a wall, his loud shouting, his slicing a fire-ladder to pieces and Gambits massive shock thrust somehow draws absolutely no attention from anyone except the main characters.
Chosen answer: Her power works by manipulating parts of the mind. Since Victor and Logan both regenerate her power can't affect them because they essentially "heal/regenerate" the part she is manipulating. Granted Prof. X threatens Logan with this in the original movies, but he is much more powerful, or could have been bluffing.